I now realize that the answer I posted previously isn't reliable, but I've found another workaround that I think is better. I'm not bothered as much by the time wasted in syntax checking of currently irrelevant schemes I as I am by the clutter in the Issue Navigator. (Everything is so incremental in Xcode nowadays that the syntax checks happen almost immediately for all schemes, and it's sometimes nice to see the effect of an edit on all schemes simultaneously.)

The workaround is to simply filter the Issue Navigator by the name of the current scheme. This can simply be copied from the desired scheme name shown in the navigator pane and pasted into the filter field at the bottom. Now you'll only see diagnostics for the chosen scheme and all others will be hidden!

It would still be nice if Xcode had a "show issues for active target only" toggle, but I find that using the filter works nicely.